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VALUATION OF CONTINGENT GUARANTEES USING LEAST-SQUARES MONTE CARLO

Part of: Mathematical finance

Published online by Cambridge University Press:  01 March 2019

T. Bienek Open the ORCID record for T. Bienek [Opens in a new window]  and
M. Scherer
T. Bienek*
Affiliation:
Lehrstuhl für Finanzmathematik, Technische Universität München, Parkring 11, 85748 Garching-Hochbrück, Germany E-Mail: tobias.bienek@tum.de
M. Scherer
Affiliation:
Lehrstuhl für Finanzmathematik, Technische Universität München, Parkring 11, 85748 Garching-Hochbrück, Germany
*
E-Mail: tobias.bienek@tum.de
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Abstract

We consider the problem of pricing modern guarantee concepts in unit-linked life insurance, where the guaranteed amount grows contingent on the performance of an investment fund that acts simultaneously as the underlying security and the replicating portfolio. Using the Martingale Method, this nonstandard pricing problem can be transformed into a fixed-point problem, whose solution requires the evaluation of conditional expectations of highly path-dependent payoffs. By adapting the least-squares Monte Carlo method for American option pricing problems, we develop a new numerical approach to approximate the value of contingent guarantees and prove its convergence. Our valuation procedure can be applied to large-scale pricing problems, for which existing methods are infeasible, and leads to significant improvements in performance.

Keywords

Fixed-point problemcontingent guaranteeleast-squares Monte Carlo

MSC classification

Primary: 91G20: Derivative securities
Secondary: 91G60: Numerical methods (including Monte Carlo methods) 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 49 , Issue 1 , January 2019 , pp. 31 - 56
Copyright
Copyright © Astin Bulletin 2019 

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